Question

Which term completes the product so that it is the difference of squares? (−5x−3)(−5x+3________) −9 −3 3 9

Answer 1

Answer:

The term that completes the product so that it is the difference of squares is 3.

Step-by-step explanation:

The term that completes the product so that it is the difference of squares is 3.

Reason:

(-5x-3)(-5x+3)=(5x)^2 - (3)^2

A difference of squares is the difference of two squared terms.

We have

a^2 - b^2

We can factorize the difference of squared terms like this:

a^2-b^2 = (a+b)(a-b)

We have (-5x-3)(-5x+3)

Lets prove it:

(-5x-3)(-5x+3) = (-5x*-5x)+(-5x*3)+(-3*-5x)+(-3*3)

(-5x-3)(-5x+3) = 25x^2+(-15x)+(15x)+(-9)

(-5x-3)(-5x+3) = 25x^2-15x+15x-9

(-5x-3)(-5x+3) = 25x^2-9

(-5x-3)(-5x+3) = (5x)^2 - (3)^2

we have that the obtained expression is a difference of squares.

Therefore the correct option is 3. The term that completes the product so that it is the difference of squares is 3 ....